在有限集上被杀死的指数为$1<\alpha<2$的渐近稳定随机游走
概率论
2019-04-24 v2
摘要
对于整数格上被吸引到指数为的严格稳定过程的随机游走，我们获得了当其命中有限集时被杀死的游走的转移概率的渐近形式。所获得的渐近形式在空间和时间变量的自然范围内一致有效。当极限稳定过程在正负两个方向均有跳跃时，情况相对简单；在另一情形下，当跳跃为单侧时，涉及相当有趣的问题，需要进行详细分析。
引用
@article{arxiv.1901.05568,
title = {Asymptotically stable random walks of index $1<\alpha<2$ killed on a finite set},
author = {Kohei Uchiyama},
journal= {arXiv preprint arXiv:1901.05568},
year = {2019}
}
备注
51 pages: this is an improved version of arXiv:1808.01484, where the RW is supposed to belong to the domain of normal attraction to a stable law, while in the present version the restriction 'normal' is removed